Split blended winglet

ABSTRACT

A split winglet configured for attachment to a wing tip of a wing. The split winglet may include an upper winglet extending from the wing tip above a chord plane of the wing and a ventral fin projecting below the chord plane. The upper winglet and the ventral fin may include tip configurations. At least one of the upper winglet tip configuration and the ventral fin tip configuration may be provided by a curved blade cap attached thereto. The curved blade cap may include a leading edge having a first curve with a first radius, and a trailing edge having a second curve with a second radius different from the first radius. The curved blade cap may also include a distal segment oblique to the first curve and the second curve.

PRIORITY

This application is a continuation of U.S. patent application Ser. No.15/090,541, filed Apr. 4, 2016, now U.S. patent Ser. No. 10/005,546,which is a continuation of U.S. patent application Ser. No. 14/452,424,filed Aug. 5, 2014, now U.S. Pat. No. 9,302,766, which is: 1) acontinuation-in-part of U.S. patent application Ser. No. 12/488,488,filed Jun. 19, 2009, now U.S. Pat. No. 9,381,999, which claims thebenefit of U.S. Provisional Application No. 61/074,395, filed Jun. 20,2008, and 2) a continuation-in-part of U.S. patent application Ser. No.13/493,843, filed Jun. 11, 2012, now U.S. Pat. No. 8,944,386, whichclaims the benefit of U.S. Provisional Application No. 61/495,236, filedJun. 9, 2011. Each of the aforementioned applications is incorporated byreference in its entirety into this application.

BACKGROUND

All aircraft wings experience drag as they move through the air. Theexperienced drag may be separated into three components: induced drag,parasitic drag, and compressibility drag. Induced drag depends on thelift force carried by the lifting surfaces. Parasitic drag arises fromcontact between a moving surface and the fluid and includes such factorsas the object form, skin friction, and interference factors.Compressibility drag is the drag associated with higher Mach numbers,which may include viscous and vortex drag, shock-wave drag, and any dragdue to shock-induced separations, all of which may vary with Machnumber. Of these, the induced drag has traditionally shown the greatestpotential for improvement through the use of winglets or other wing tipdevices.

Generally, an aircraft's wing may be swept to reduce compressibilitydrag effects on high-speed airplanes. A swept wing is generally designedso the angle between the aircraft's body and the wing is oblique, andspecifically is swept toward the aft of the aircraft. The sweep of thewing's leading edge and trailing edge does not necessarily have to be atthe same angle. A wing tip device may also be added to further reducethe drag on the wing. One alternative is to provide a raked wing tip. Araked wing tip conventionally has a higher degree of sweep than the restof the wing. Winglets are also an alternative solution, generally usedto increase the effective aspect ratio of a wing, with less structuralimpact than adding wingspan. Winglets are generally near verticalextensions of the wing tip. Wing tip devices may increase the liftgenerated at the wing tip, and reduce the induced drag caused by wingtipvortices, improving the lift-to-drag ratio. Although winglets reducedrag generated by wingtip vortices, winglets produce lift that increasesthe bending moment on the wing.

Various wing tip devices and geometries are described, for example, inU.S. Pat. No. 7,971,832 (titled “Wing Tip Devices,” issued Jul. 5,2011), US 2007/0114327 (titled “Wing Load Alleviation Apparatus andMethod,” published May 24, 2007), U.S. Pat. No. 6,722,615 (titled “WingTip Extension for a Wing,” issued Apr. 20, 2004), U.S. Pat. No.6,827,314 (titled “Aircraft with Active Control of the Warping of ItsWings,” issued Dec. 7, 2004), U.S. Pat. No. 6,886,778 (titled “EfficientWing Tip Devices and Methods for Incorporating such Devices intoExisting Wing Designs,” issued May 3, 2005), U.S. Pat. No. 6,484,968(titled “Aircraft with Elliptical Winglets,” issued Nov. 26, 2002), andU.S. Pat. No. 5,348,253 (titled “Blended Winglet,” issued Sep. 20,1994), each of which is incorporated by reference into this applicationas if fully set forth herein.

SUMMARY

Embodiments described herein may be applied to a wing or wingletincorporating a tip device with a curved leading edge and a curvedtrailing edge to minimize induced drag for a given wing form. The curvedleading edge is designed to achieve optimal results such as, forexample, maintaining attached flow, minimizing flow separation, andminimizing premature vortex roll-up, while the curved trailing edge isdesigned to achieve optimal results such as, for example, keeping thechord distribution consistent with an elliptic loading over theplanform. The curve of the leading and trailing tip sections may bedescribed generally as parabolic, and preferably as super elliptic. Afinite tip segment may be included with a sweep angle approximate to thetrailing edge sweep angle. This finite section may be used to assist instabilizing the tip vorticity and maintain the vortex position close tothe extreme wing tip.

Aerodynamic loading may be important to achieving optimum wingperformance; however, the effect of the actual loading obtained inflight at a wing tip is usually overlooked. Failure to achieve theoptimum elliptic loading, particularly near the tip of the wing, maylead to premature tip vortex formation and a corresponding increase ofinduced drag. This characteristic may also apply to planar wings wherepremature tip vortex roll-up, inboard of the wing tip, is frequentlyvisible as a condensation trail in flight.

Embodiments described herein may be applied to the tip of a flat wing orto a winglet. However, aspects of the design may be applied to liftingsurfaces in general, and particularly to dynamic lifting surfaces.Alternatively, aeronautical propulsion systems, including, for example,propellers and helicopters rotors, may alternatively benefit equallyfrom aspects of the design and are additionally considered within thescope of the invention. Embodiments described herein may also apply toany applications which use either static or dynamic lifting surfacessuch as ship propellers.

Embodiments described herein comprise an innovative winglet conceptincluding a split winglet, which includes separate extensions above andbelow the wing chord plane. The split winglet includes an upward slopingelement similar to an existing winglet and a down-ward canted element(ventral fin). The ventral fin counters vortices generated byinteractions between the wingtip and the lower wing surface.

The split winglet is designed to reduce drag but without generating theincreased bending moment found in existing winglet designs. The splitwinglet design is believed to improve fuel burn or reduce fuel burn byapproximately 1.5%, reduce drag by up to 9.5% over a wing with astandard tip, and improve cruise performance by more than 40% overexisting blended-winglet configurations.

Embodiments as described herein are adaptable to various wing and wingtip designs. Embodiments may include an integrated split blended wingletthat attaches as a single unit at a wing tip, and may include a separateventral fin designed to attach to an existing blended winglet.

An apparatus is provided herein for a split winglet configured forattachment to a wing tip of an airplane. The split winglet comprises anupper winglet extending from the wing tip above a chord plane of thewing and a ventral fin projecting below the chord plane from a lowersurface of the upper winglet. Generally, the upper winglet furthercomprises a transition section which curves upward from the wing tipinto a substantially planar section. In an embodiment, the ventral finprojects below the chord plane from substantially at or near themidpoint of the transition section. An upper surface and the lowersurface of the upper winglet are respective smooth extensions of anupper surface and a lower surface of the wing tip. The upper surface andthe lower surface of the upper winglet are bounded by a leading edge anda trailing edge. The leading edge and the trailing edge generally arelinear sections which are swept toward an airstream directionsubstantially parallel with the root chord and converging at an upperwinglet tip configuration. In an embodiment, the leading and trailingedges of the upper winglet respectively are continuous extensions of aleading edge and a trailing edge of the wing. The upper winglet tipconfiguration comprises the leading and trailing edges curving towardthe airstream direction and then converging to substantially a pointdistal of the wing tip of the airplane. Similarly, the ventral fincomprises an upper surface and a lower surface bounded by a leading edgeand a trailing edge both converging at a ventral fin tip configurationcomprising the leading and trailing edges curving toward the airstreamdirection and then terminating at substantially a point distal of thewing tip of the airplane. In one embodiment, the leading edge of theventral fin merges into the lower surface of the upper winglet distal ofthe leading edge of the upper winglet, and the trailing edge of theventral fin merges into the trailing edge of the upper winglet. Inanother embodiment, the leading edge of the upper winglet and theleading edge of the ventral fin merge together at the transitionsection, such that the leading edges of the upper winglet and theventral fin are continuous extensions of the leading edge of the wing.Similarly, the trailing edge of the upper winglet and the trailing edgeof the ventral fin may merge together at the transition section, suchthat the trailing edges of the upper winglet and the ventral fin arecontinuous extensions of the trailing edge of the wing.

In an exemplary embodiment, a split winglet configured for attachment toa wing tip of an airplane comprises an upper winglet extending from thewing tip above a chord plane of the wing. The upper winglet comprisingan upper surface and a lower surface bounded by a leading edge and atrailing edge, the leading edge and the trailing edge converging to anupper winglet tip configuration. A ventral fin projecting from the lowersurface of the upper winglet comprises an upper surface and a lowersurface bounded by a leading edge and a trailing edge extending belowthe chord plane. The leading edge and the trailing edge converging to aventral fin tip configuration. The upper surface and the lower surfaceof the upper winglet respectively merge with an upper surface and alower surface of the wing.

In another exemplary embodiment, the leading edge and the trailing edgeof the upper winglet comprise substantially linear sections which areswept toward an airstream direction being substantially parallel withthe root chord and then converge to the upper winglet tip configuration.In another exemplary embodiment, the upper winglet tip configurationcomprises the leading edge and the trailing edge curving toward theairstream direction and then converging to substantially a point distalof the wing tip of the airplane. In another exemplary embodiment, theupper winglet tip configuration comprises a curve of the leading edgehaving a first radius and a curve of the trailing edge having a secondradius, wherein the first radius and the second radius orient theleading and trailing edges toward the airstream direction so as toconverge to substantially a point distal of the wing tip of theairplane.

In another exemplary embodiment, the leading edge and the trailing edgeof the ventral fin comprise substantially linear sections which areswept toward an airstream direction being substantially parallel withthe root chord and then converge to the ventral fin tip configuration.In another exemplary embodiment, the ventral fin tip configurationcomprises the leading edge and the trailing edge curving toward theairstream direction and then converging to substantially a point distalof the wing tip of the airplane.

In another exemplary embodiment, the upper winglet further comprises atransition section which curves upward from the wing tip into asubstantially planar section, such that the upper surface and the lowersurface of the upper winglet respectively are smooth extensions of theupper and lower surfaces of the wing tip, and such that the leading andtrailing edges of the upper winglet respectively are continuousextensions of a leading edge and a trailing edge of the wing. In anotherexemplary embodiment, the transition section comprises a substantiallyconstant radius of curvature between the wing tip and the planarsection. In another exemplary embodiment, the transition sectioncomprises one or more radii of curvature disposed along a length of thetransition section between the wing tip and the planar section. Inanother exemplary embodiment, the transition section comprises asubstantially nonlinear curvature along a length of the transitionsection between the wing tip and the planar section. In anotherexemplary embodiment, the ventral fin projects from the lower surface ofthe transition section and extends below the chord plane. In anotherexemplary embodiment, the leading edge of the ventral fin merges intothe lower surface of the upper winglet distal of the leading edge of theupper winglet. In another exemplary embodiment, the trailing edge of theventral fin merges into the trailing edge of the upper winglet. Inanother exemplary embodiment, the leading edge of the upper winglet andthe leading edge of the ventral fin merge together at the transitionsection, such that the leading edge of the upper winglet and the leadingedge of the ventral fin are continuous extensions of the leading edge ofthe wing. In another exemplary embodiment, the trailing edge of theupper winglet and the trailing edge of the ventral fin merge together atthe transition section, such that the trailing edge of the upper wingletand the trailing edge of the ventral fin are continuous extensions ofthe trailing edge of the wing.

In an exemplary embodiment, a wing tip of an airplane comprises an upperwinglet extending from the wing tip above a chord plane of the wing andconverging at an upper tip configuration comprising a curving of theupper winglet toward an airstream direction being substantially parallelwith the root chord. A ventral fin projecting below the chord plane fromthe upper winglet and converging at a ventral fin tip configurationcomprising a curving of the ventral fin toward the airstream direction.

In another exemplary embodiment, the upper winglet comprises an uppersurface and a lower surface proximally bounded by a leading edge anddistally bounded by a trailing edge, the leading and trailing edgesbeing swept toward the airstream direction, wherein the upper surfaceand the lower surface are smooth extensions of an upper surface and alower surface of the wing. In another exemplary embodiment, the upperwinglet further comprises a curved transition section extending from thewing to a substantially planar section converging at the upper tipconfiguration, and wherein the ventral fin projects below the chordplane from substantially at or near the midpoint of the curvedtransition section. In another exemplary embodiment, the ventral fincomprises an upper surface and a lower surface proximally bounded by aleading edge and distally bounded by a trailing edge, the leading andtrailing edges being swept toward the airstream direction and convergingat the ventral fin tip configuration.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings refer to embodiments of the present invention in which:

FIG. 1 is a perspective view of an exemplary airplane including wing tipgeometry according to embodiments described herein;

FIG. 2A is an enlarged top view of an exemplary embodiment of a wing tipaccording to aspects of the embodiments described herein;

FIG. 2B is a cross-sectional view of the wing tip illustrated in FIG.2A, taken along line P-P;

FIG. 3 is an enlarged trailing-edge view of an exemplary embodiment of awing tip comprising a spanwise camber, according to embodimentsdescribed herein;

FIG. 4A is an enlarged top view of an exemplary embodiment of a wing tipaccording to aspects of the embodiments described herein;

FIG. 4B is a cross-sectional view of the wing tip illustrated in FIG.4A, taken along line M-M;

FIG. 5 is an enlarged trailing-edge view of an exemplary embodiment of awing tip comprising a spanwise camber, according to embodimentsdescribed herein;

FIG. 6A is a perspective view a representative wing with a winglet endsection according to embodiments described herein;

FIG. 6B is a trailing-edge view of the winglet of FIG. 6A, illustrated aspanwise camber of the winglet in accordance with aspects of the presentinvention;

FIG. 7 illustrates a perspective view of an airplane comprising anexemplary embodiment of a propeller, in accordance with the presentinvention;

FIG. 7A is an enlarged section view of a propeller tip geometry of theexemplary propeller illustrated in FIG. 7;

FIG. 8 illustrates a perspective view of a helicopter comprising anexemplary embodiment of a rotor according to the present invention;

FIG. 8A is an enlarged section view of a rotor tip geometry of theexemplary rotor illustrated in FIG. 8;

FIG. 9A is a front profile view of an exemplary embodiment of a splitwinglet in accordance with the present invention;

FIG. 9B is a bottom view of the embodiment of the split wingletillustrated in FIG. 9A;

FIG. 9C is a side view of the embodiment of the split wingletillustrated in FIGS. 9A-9B;

FIG. 10 illustrates an exemplary load distribution along a wing whichincludes the exemplary embodiment of the split winglet illustrated inFIGS. 9A-9C;

FIG. 11A is a front profile view of an exemplary embodiment of anintegrated split winglet in accordance with the present invention;

FIG. 11B is a side view of the embodiment of the integrated splitwinglet illustrated in FIG. 11A;

FIG. 12 illustrates an airplane comprising an exemplary embodiment of asplit winglet in accordance with the present invention;

FIG. 13 illustrates an exemplary embodiment of a split wingletcomprising a tip configuration according to embodiments of the presentinvention;

FIG. 14 illustrates an exemplary use environment wherein an airplanecomprises a split winglet including a curved blade tip configuration inaccordance with an embodiment of the present invention;

FIG. 15A is a front profile view of an exemplary embodiment of a splitwinglet comprising a curved blade tip configuration in accordance withthe present invention;

FIG. 15B is a bottom view of the embodiment of the split wingletillustrated in FIG. 15A;

FIG. 15C is a side view of the embodiment of the split wingletillustrated in FIGS. 15A-15B;

FIG. 16A is an enlarged section view of a winglet tip cap of an upperwinglet illustrated in FIG. 9C; and

FIG. 16B is an enlarged section view a curved blade cap installed ontothe upper winglet illustrated in FIG. 16A.

While the present invention is subject to various modifications andalternative forms, specific embodiments thereof have been shown by wayof example in the drawings and will herein be described in detail. Theinvention should be understood to not be limited to the particular formsdisclosed, but on the contrary, the intention is to cover allmodifications, equivalents, and alternatives falling within the spiritand scope of the present invention.

DETAILED DESCRIPTION

In the following description, numerous specific details are set forth inorder to provide a thorough understanding of the present invention. Itwill be apparent, however, to one of ordinary skill in the art that thepresent invention may be practiced without these specific details. Inother instances, specific numeric references such as “first winglet,”may be made. However, the specific numeric reference should not beinterpreted as a literal sequential order but rather interpreted thatthe “first winglet” is different than a “second winglet.” Thus, thespecific details set forth are merely exemplary. The specific detailsmay be varied from and still be contemplated to be within the spirit andscope of the present invention. The term “coupled” is defined as meaningconnected either directly to the component or indirectly to thecomponent through another component. Further, as used herein, the terms“about,” “approximately,” or “substantially” for any numerical values orranges indicate a suitable dimensional tolerance that allows the part orcollection of components to function for its intended purpose asdescribed herein.

In general, an apparatus is provided for a split winglet configured forattachment to a wing tip of an airplane. The split winglet comprises anupper winglet smoothly extending from the wing tip above a chord planeof the wing and a ventral fin projecting below the chord plane from alower surface of the upper winglet. Generally, the upper winglet furthercomprises a transition section which curves upward from the wing tipinto a substantially planar section. In an embodiment, the ventral finprojects below the chord plane from substantially a midpoint of thetransition section. The upper winglet comprises a transition sectionwhich curves upward from the wing tip into a substantially planarsection. Upper and lower surfaces of the upper winglet are bounded byleading and trailing edges which are swept toward an airstreamdirection, parallel with the root chord, and curve toward the airstreamdirection before terminating at a point distal of the wing tip. In anembodiment, the leading and trailing edges of the upper wingletrespectively are continuous extensions of a leading edge and a trailingedge of the wing. Similarly, upper and lower surfaces of the ventral finare bounded by leading and trailing edges which curve toward theairstream direction and terminate at a point distal of the wing tip.

The following description should be read with reference to the drawings,in which like elements in different drawings are identically numbered.The drawings, which are not necessarily to scale, depict selectedembodiments and are not intended to limit the scope of the invention.For instance, edges appearing be pointed in the drawings may inactuality be rounded (e.g., leading edges in FIG. 2B, FIG. 3, FIG. 4B,and FIG. 5). The description illustrates by way of example, not by wayof limitation, the principles of the invention. This description willclearly enable one skilled in the art to make and use the invention, anddescribes several embodiments, adaptations, variations, alternatives,and uses of the invention, including what is presently believed to bethe best mode of carrying out the invention.

Embodiments described herein include an optimum wing tip geometry forwings. The described geometry may reduce induced drag associated withpremature tip vortex formation from suboptimum aerodynamic loading.Embodiments of the tip design geometry may preserve an elliptic loaddistribution to the tip of the wing. In addition, airfoil sections maybe cambered and twisted so as to avoid flow separation along highlyswept leading edges, thereby maintaining an elliptic loading to theextreme tip. Spanwise camber of lifting surfaces may also beincorporated to maintain flow attachment and avoid premature roll-up oftip vorticity.

Based on aerodynamic analysis of embodiments incorporating aspects ofthe present invention, it has been observed that significant reductionsof induced drag can be expected relative to that found in typicalcurrent wingtip designs. These results may depend upon the properselection of parameters that define the tip geometry and are discussedbelow. The potential benefits may be expected in the range of about −1%to about −3% induced drag reduction relative to a standard winglet for acommercial transport airplane configuration. The induced drag reductionmay correspond to an increase in fuel efficiency in the range of about0.7% to about 2% at normal cruising speeds. Additional benefits may beexpected for low-speed operation.

Although embodiments of the invention are typically described in termsof wingtip devices, or winglets, the invention is not so limited.Aspects of the invention may be applied to lifting surfaces in general,and particularly to wings, and more particularly to aircraft, includingplanar wings without the use of winglets. Aeronautical propulsionsystems, including, for example, propellers and helicopter rotors, mayalternatively benefit equally from aspects of the invention and areadditionally considered within the scope of the invention. Embodimentsof the present invention may also apply to any applications which useeither static or dynamic lifting surfaces such as helicopter rotors,ship propellers, and the like. Finally, other applications that maybenefit from aspects of the invention include devices intended to moveair or fluid, such as, by way of non-limiting example, fans.

Reference axes are used generally to orient the description, as known inthe art, and therefore include a reference system for an exemplaryairplane generally, a reference system for a wing of the airplane, and areference system for a tip of the wing. As illustrated in FIG. 1, anairplane reference system is used to orient the description with respectto the aircraft. An x-axis runs along a longitudinal axis of theairplane from nose to the tail. A y-axis is perpendicular to the x-axisand is horizontally oriented relative to the airplane. Finally, a z-axisis orthogonal to both the x- and y-axes, oriented in the verticaldirection. A wing reference system may also be used which generallydiffers from the airplane reference system, as it lies in the referenceplane of the wing. Therefore, as illustrated in FIGS. 3 and 5, the wingreference system generally is rotated by an incidence angle, a dihedralangle, and a sweep angle. Finally, for embodiments described herein, asillustrated in FIGS. 2 and 4, an origin of a reference system for a wingtip geometry is coincident with the beginning of the wing tip geometryand lies generally in the plane of the wing, at the wing tip. However,this relationship may change substantially from the wing referencesystem in cases of winglet applications (e.g., as shown in FIG. 6).Generally, the wing tip reference system has its origin at the beginningof a curved leading edge of the wing tip, or a curved trailing edge,whichever is closer to the airplane. The x′-y′ axis is then in the planeof the wing at the origin of the wing tip. Therefore, the wing tipgeometry may be rotated from the airplane reference system by the sweepangle, the dihedral angle, an incidence angle, and a winglet angle, anddisplaced from the airplane reference system by the length of the wingto the wing tip.

FIG. 1 illustrates an exemplary airplane 102 including a wing tipsection 100 according to embodiments described herein. The wing tipsection 100 may be designed to minimize induced drag by preserving anelliptic load distribution. A leading edge 104 of the wing tip section100 may be curved to avoid flow separation. A trailing edge 106 of thewing tip section 100 may be curved to maintain a desired chordvariation. A trailing edge tip segment 108 may have a small, but finitedimension and sweep. The trailing edge tip segment 108 may be swept atan angle approximately the same or similar angle as a trailing edgesweep angle. The tip segment 108 may assist in stabilizing vorticity atthe tip and maintain its position at the trailing edge.

A wing 110 has a leading edge 112 and a trailing edge 114. The leadingedge 112 may be substantially straight, and may transition into thecurved leading edge 104 of the wing tip section 100. The trailing edge114 may be substantially straight before transitioning into the curvedtrailing edge 106 of the wing tip section 100. The leading edge 112 andthe trailing edge 114 may also be swept. However, the leading edge 112and the trailing edge 114 may be swept at different angles. For example,the leading edge 112 may comprise a greater sweep angle than a sweepangle of the trailing edge 114.

FIG. 2A is an enlarged top view of an exemplary embodiment of a wing tipgeometry 200 according to aspects of the embodiments described herein.An x′-y′ reference system for the wing tip geometry 200 may be createdby a line parallel 202 and another line perpendicular 204 to thelongitudinal axis of the airplane body. An x′-y′ reference plane formedby the lines 202, 204 is within a plane of a wing 210. In someembodiments, the wing 210 is not perpendicular to the plane body, but isswept distally toward the rear of the airplane. The wing 210 may also berotated upward at a dihedral angle, or tilted about a pitch axis of theairplane to create an incidence angle. In the illustrated embodiment ofFIG. 2A, a leading edge 212 of the wing 210 is swept at an angle,Λ_(LE), 214, relative to the y′-reference axis 204, and a trailing edge216 is swept at an angle, Λ_(TE), 218, relative to the y′-reference axis204. The sweep angle of the leading edge 214 and the trailing edge 218may be at the same angle or different angles. Preferably, the sweepangle of the leading edge 214 is greater than the sweep angle of thetrailing edge 218.

In one embodiment, the tip of the wing 210 has a wing tip geometry 200that curves distally toward the rear of the airplane. The wing tipgeometry 200 begins along the leading edge at a point 224 and along thetrailing edge at a point 226. The points 224, 226 do not necessarilyhave to be located at the same distance away from the body of theairplane. In some embodiments, for example, the point 224 may be locatedcloser to the body of the airplane than point 226. A curved leading edge220 and a curved trailing edge 222 begin tangentially with the leadingedge 212 and the trailing edge 216, respectively, and then curvedistally toward the rear of the airplane. The curved leading edge 220and curved trailing edge 222 smoothly transition from the substantiallystraight leading and trailing edges 212, 216, respectively, then slopedistally along a substantially parabolic curve approaching a free streamvelocity direction U 230, and then terminate at an end segment 234 BD.As illustrated in FIG. 2A, the curved leading edge 220 terminates at aleading edge tip 228, and the curved trailing edge 222 terminates at atrailing edge tip 232. Preferably, the curved leading edge 220 is moreclosely aligned with the direction of the free stream velocity U230 thanis the curved trailing edge 222, such that the leading edge tip 228 isdistal of the trailing edge tip 232.

In the illustrated embodiment of FIG. 2A, the end segment 234 BD,between the leading edge tip 228 and the trailing edge tip 232, islocated distal of the curved trailing edge 222. In some embodiments, theend segment 234 BD may have a specified length and may be swept at anangle substantially equal to the angle, Λ_(TE), 218 of the trailing edge216. A reference length h 252 corresponds to a height of the leadingedge tip 228 above the point 226 along the trailing edge of the wing210, and thus may be used as a measure of the height of the end segment234 BD above the point 226. A preferred ratio of the end segment 234 BDto the length his in the range of 0.15<BD/h<0.20 with the ratio trendinghigher at higher values of tip lift coefficients. Observations indicatethat the end segment 234 configured as in the illustrated embodimentadvantageously stabilizes the tip vortex.

It will be recognized that the wing tip section 200 may be applied to aconventional flat wing, wherein the curved leading edge 220 and thecurved trailing edge 222 lie in the wing reference plane (i.e., thex′-y′ plane). In such an embodiment, the entire wing, emanating from thebody of the airplane and terminating at the end segment 234, ispositioned substantially in the same plane. In an alternate embodiment,the wing tip section 200 may be applied to a conventional winglet,wherein an end of the wing projects out of the x′-y′ reference plane, inthe z′-direction. Further, the wing tip section 200 may be integrallyformed with the rest of the wing 210, or may comprise a separateassembly which is attached or adhered to the tip of the wing. The wingtip section 200 may be attached by way of bolting, welding, or any otherknown practice of attaching wing segments.

FIG. 2B is a cross-sectional view of the wing tip section 200, takenalong line P-P of FIG. 2A. A chord, represented by dotted line 236,extends from the curved leading edge 220 to the curved trailing edge222, and is oriented at an angle ϕ_(T) relative to the x′-reference line202. The chord distribution conforms to the optimum aerodynamic loadingon the wing surface. In one embodiment, the curved trailing edge 222 isdesigned to maintain a desired chord distribution to achieve ellipticloading. In other embodiments, airfoil sections may also be incorporatedat specified locations, corresponding to the local chord line and thetwist angle ϕ_(T) distribution.

These features may be alternatively described in mathematical terms,where all dimensions may be normalized relative to a tip extensionlength, g 250. The tip extension length g 250 is a straight-linedistance of the trailing edge which extends past the trailing edgeorigin 226 of the wing tip geometry 200. As shown in FIG. 2A, the tipextension length 250 is the x′-direction distance between the origin 226of the wing tip along the trailing edge 222 and the leading edge tip228. As indicated above, the reference length h 252 corresponds to aheight of the tip extension length, and thus is the y′-distance from thecurved wing tip section 200 origin along the trailing edge, point 226,to the leading edge tip 228. Points A, B, C, D, and E are added forreference locations. Point A 224 is the point where the leading edge 212transitions into the curved leading edge 220, and deviates from a linetangential with the leading edge 212. Reference point C 226 is thecorresponding point along the trailing edge 216. Point B 228 is the endof the curved leading edge 220, while point D 232 is the end of thecurved trailing edge 222. The segment BD is the end segment 234.

In some embodiments, the curved leading edge 220, from point A to B, maybe defined by:X−x _(A)=tan Λ_(LE)(y−y _(A))+M ₁(y−y _(A))^(m) ¹ +M ₂(y−y _(A))^(m) ² .

In one embodiment, the curved leading edge parameters M₁ and m₁, M₂ andm₂ are selected to define a planform that may maintain attached flow andavoid flow separation. The parameters are therefore chosen so as tocreate a smooth parabolic transition from the substantially straightleading edge 212 to a desired end slope at point B 228. A desiredleading edge slope, dy/dx, at point B approaches the free streamdirection U230 and may be in the range of about 0.0 to about 0.1, and ispreferably in the range about 0.03 to about 0.07. In one embodiment, thedesired leading edge slope approaches about 0.05. To provide optimalperformance characteristics, where x_(A), y_(A), g, and Λ_(LE) aregiven, M₁ is in the range of about 0.4 to about 0.6, M₂ is in the rangeof about 0.08 to about 0.12, m₁ is in the range of about 3.6 to about5.4, and m₂ is in the range of about 5.2 to about 7.7. Preferably, M₁ isabout 0.5, M₂ is about 0.1, m₁ is about 4.5, and m₂ is about 6.5. Theinclusion of two power terms is preferred to sufficiently providecontrol of the leading edge slope, dy/dx at point B and to match theoptimum leading edge curve shape. The design includes at least one powerterm so as to create the smooth parabolic transition from the leadingedge to the end point B 228. However, in other embodiments, power termsmay be removed or added so as to further approach optimal performance.

The curved trailing edge 222, from point C to D, may be defined by:x−x _(C)=tan Λ_(TE)(y−y _(C))+N ₁(y−y _(C))^(n) ¹ +N ₂(y−y _(C))^(n) ² .

In one embodiment, the curved trailing edge parameters N₁ and n₁, N₂ andn₂ are selected so as to maintain an appropriate chord variation andcontrol of a trailing edge slope, dy/dx, approaching point D. Theparameters are chosen to provide a smooth parabolic transition from thesubstantially straight trailing edge 216 to the curved trailing edge 222so as to achieve elliptic loading over the wing tip section 200. Theparameters may additionally be chosen so as to control an approach ofthe trailing edge slope at point D toward the free stream direction 230.For example, in some embodiments, the trailing edge slope at point D mayfall within the range of about 0.0 to about 2.0. In one embodiment, thetrailing edge slope approaching point D is in the range of about 0.06 toabout 0.15, and is preferably about 0.10. To provide optimal performancecharacteristics, where x_(C), y_(C), segment BD, h, and Λ_(TE) aregiven, N₁ is in the range of about 0.08 to about 0.12, N₂ is in therange of about 0.16 to about 0.24, n₁ is in the range of about 2.8 toabout 4.2, and n₂ is in the range of about 3.6 to about 5.4. Moreparticularly, N₁ is about 0.1, N₂ is about 0.2, n₁ is about 3.5, and n₂is about 4.5. The inclusion of two power terms are preferred so as tosufficiently control the loading on the wing tip section 200 andmaintain an appropriate chord variation. However, fewer or additionalpower terms may be removed or added to more particularly control thesefeatures. It will be appreciated that at least one power term shouldremain so as to achieve a parabolic transition from trailing edge totip.

The end segment BD, may have a small but finite dimension and may beswept at an angle approximate to the trailing edge angle, Λ_(TE), 218.This end segment BD may assist in stabilizing the tip vorticity andmaintain the vortex position very close to the leading edge tip 228, atpoint B. It will be recognized that the length of segment BD may bedetermined by way of other parameters herein described above.

The airfoil sections may be cambered or twisted so as to maintain anelliptic loading of the wing tip section 200 and to avoid flowseparation along the curved leading edge 220. The wing chord,represented by the dotted line 236, may be designed according to theparameters above to maintain the desired chord distribution. In someembodiments, the airfoil may additionally be twisted by an angle ϕ_(T),thereby angling the chord relative to the free stream direction 230.Airfoil twist may be defined by the rotation angle of the airfoil chordabout the tip trailing edge, CDB, relative to the wing reference plane,x′-y′ plane. In other embodiments, airfoil shapes may be modifiedvariations of the winglet airfoil disclosed herein without deviatingfrom the present invention.

FIG. 3 is an enlarged trailing-edge view of an exemplary embodiment of awing tip section 300 of a wing 310 which comprises a spanwise camber,according to the present invention. The spanwise camber may be generatedby a curve in the z′-direction, of a curved trailing edge 322 of thewing tip section 300 from the wing reference plane, x′-y′. In oneembodiment, the curve in the z′-direction, lying in the y′-z′ plane,begins tangentially from a wing trailing edge 316 at a point 326 andthen deviates parabolically before terminating at a trailing edge endpoint 332. Therefore, in the illustrated embodiment, the end of the wingtip section 300 curves out of the x′-y′ reference plane, therebygenerating a wing tip surface which is substantially cylindrical untilthe trailing edge terminates at point 332. In another embodiment, thespanwise camber creates part of a cylindrical surface, which may beaugmented by superposition of airfoil camber and twist.

The representative profile of a wing according to aspects of embodimentsdescribed herein, including a spanwise camber, may alternatively bedescribed in mathematical terms. In some embodiments, the wing 310 mayinclude a slight incline ϕ_(D), the dihedral angle 350, from horizontal352, as the wing approaches the wing tip section 300. In someembodiments, the wing tip section 300 may also, or alternativelyincorporate a spanwise camber so as to maintain flow attachment, reduceflow separation, and minimize premature roll-up along the outer edge ofthe wing tip section 300.

The camber may be defined in terms of vertical displacement, z, of thecurved trailing edge CD from a straight line extension of the wingtrailing edge 316, along the y′-axis, and may be defined by:z−z _(C) =−P(y−y _(C))^(p), where y _(C) <y<y _(D).

In one embodiment, the parameters P and p, are selected in combinationwith the wing incline and twist so as to define the lifting surfacebetween the previously defined curved leading and curved trailing edges.In an exemplary embodiment characterized by optimal performance, whereinx_(C), y_(C), segment BD, h, and Λ_(TE) are given, P is in the range ofabout 0.12 to about 0.18, and p is in the range of about 2.0 to about3.0. Preferably, P is about 0.15, and p is about 2.5. In otherembodiments, the wing tip section 300 may be curved in the oppositedirection, or in the positive z-direction, according to the sameprinciples described herein. Moreover, in some embodiment, the abovecombination of parameters may be defined in relation to a wing planform(i.e., sweep and taper) and aerodynamic loading so as to maintain theelliptic loading and attached flow to the wing tip section 300. It willbe appreciated that the above-discussed design parameters may bespecified within appropriate limits to provide optimal performancecharacteristics.

FIG. 4A is an enlarged top view of an exemplary embodiment of a wing tipsection 400 of a wing 410 according to aspects of the embodimentsdescribed herein. The wing 410 includes a substantially straight leadingedge 412, swept rearward at an angle Λ₁ 414 and a trailing edge 416,which is also substantially straight and swept rearward at an angle Λ₂418. In one embodiment, the wing tip section 400 begins at point 424along the leading edge 412, and a point 426 along the trailing edge 416.The points 424 and 426 may be located at the same distance away from theairplane body, as in the illustrated embodiment, or may be located atdifferent distances from the airplane body. For example, in anembodiment, the point 424 may be located as shown, but the point 426along the trailing edge 416 may be located further away from theairplane body. In the illustrated embodiment, the wing tip section 400includes a curved leading edge 420 and a curved trailing edge 422. Thecurved leading edge 420 emanates from a line tangential with the leadingedge 412 and smoothly transitions along an elliptical curve to anendpoint 428. A slope of the curved leading edge 420 nearing the point428 approaches the free stream direction U. Similarly, the curvedtrailing edge 422 emanates tangentially from the trailing edge 416 andcurves rearward along an elliptical curve to an endpoint 432, where aslope of the curved tailing edge 422 nearing the end point 432 alsoapproaches the free stream direction U. As will be appreciated, theslope approaching the wing tip is not necessarily the same along thecurved leading edge 420 and the curved trailing edge 422.

In one embodiment, an end segment 434, between the leading edge tip 428and the trailing edge tip 432, may be located distally of the curvedtrailing edge 422. In some embodiments, the segment 434 may have aspecified length and may be swept at an angle substantially equal to thewing trailing edge sweep angle 418. Preferably, the end segment 434 hasa length in a range of 0.15<CE/h<0.20, wherein the ratio trends higherat higher values of tip lift coefficients. Observations indicate that anend segment such as CE 434 advantageously stabilizes the tip vortex.

The embodiment illustrated in FIG. 4A may also be described inmathematical terms so as to define an optimal design which maintains anattached flow and avoids premature vortex roll-up. Points A, B, C, D,and E along with lengths C₁, C₂, g, and h are included for reference. Asdescribed above, point A 424 and point D 426 are the respective originsof the curved end section 400 along the leading edge 412 and thetrailing edge 416. Points C 428 and E 432 are the respective end tiplocations of the curved leading edge 420 and the curved trailing edge422, respectively. Point B is a location along the curved leading edge420 corresponding to the same y′-distance as point E of the curvedtrailing edge 422. Reference length C₁ is the distance along thex′-direction between reference points A and D, while reference length C₂is the distance along the x′-direction between points B and E. Referenceheight h is the y′-direction distance from the origin along the trailingedge, point D, to the curved wing tip extreme end, point C. Referencedistance g is the x′-direction distance from point D to the curvedleading edge end point C.

The leading curved edge 420, from point A to C, may be defined by:x−x _(A) y−y _(A)] tan Λ₁ +a ₁[(1−([y−y _(A)]/b ₁)^(n) ¹ )^((1/m) ¹⁾−1].

In one embodiment, the curved leading edge geometry parameters a₁, b₁,m₁, and n₁ are selected so as to define a planform which maintains anattached flow and reduce flow separation, while minimizing prematurevortex roll up. As will be recognized, the inclusion of these fourparameters is sufficient to provide control of the leading edgecurvature near point A, and the contour slope at point C, so as todefine an optimal leading edge contour. In other embodiments, additionalterms may be added or removed so as to further refine the optimumparameters.

Sizing parameters (g/C₁), (h/C₁), (dy/dx)_(C), and (C₂/C₁) relate tooverall planform proportions and provide a framework for optimizingcontours for both leading edge 420 and the trailing edge 422. In anexemplary embodiment characterized by acceptable performance levels,(g/C₁) is in the range of about 0.50 to about 0.80, (h/C₁) is in therange of about 0.60 to about 1.00, (dy/dx)_(C) is in the range of about0.03 to about 0.07, and (C₂/C₁) is in the range of about 0.60 to about0.70. In one embodiment, (g/C₁) is about 0.60, (h/C₁) is about 0.70,(dy/dx)_(C) is about 0.05, and (C₂/C₁) is about 0.65.

Leading edge contour parameters (a₁/C₁), (b₁/C₁), m₁, and n₁ define theleading edge contour within the sizing framework. In an exemplaryembodiment characterized by acceptable performance levels, (a₁/C₁) is inthe range of about 1.50 to about 2.50, (b₁/C₁) is in the range of about0.60 to about 0.90, m₁ is in the range of about 2.0 to about 4.0, and n₁is in the range of about 1.50 to about 3.0. In one embodiment, (a₁/C₁)is about 2.0, (b₁/C₁) is about 0.70, m₁ is about 3.0, and n₁ is about2.0.

The curved trailing edge 422, from point D to E, may be defined by:x−x _(D) =y tan Λ₂ +a ₂[(1−([y−y _(D)]/b ₂)^(n) ² )^((1/m) ² ⁾−1].

In an embodiment, the trailing edge curvature near point D and thecontour slope near point E are defined so as to achieve a chorddistribution consistent with an elliptical loading over the planform tominimize drag, thereby providing optimal performance characteristics.

Sizing parameters (g/C₁), (h/C₁), (dy/dx)_(E), and (C₂/C₁) relate tooverall planform proportions and provide a framework for optimizingcontours for both the leading edge 420 and the trailing edge 422. Thesesizing parameters, with the exception of (dy/dx)_(E), have beenpreviously selected, as discussed above in terms of the curved leadingedge geometry. Sizing parameter (dy/dx)_(E) is acceptable within therange of about 0.06 to about 0.15, and is preferably about 0.10.Therefore, contour parameters, (a₂/C₁), (b₂/C₁), m₂, and n₂ remain to beselected. The trailing edge contour parameters (a₂/C₁), (b₂/C₁), m₂, andn₂ define the trailing edge contour within the sizing framework. In anexemplary embodiment characterized by acceptable performance levels,(a₂/C₁) is in the range of about 0.80 to about 1.50, (b₂/C₁) is in therange of about 0.30 to about 0.60, m₂ is in the range of about 1.50 toabout 2.50, and n₂ is in the range of about 1.50 to about 2.50. In oneembodiment, (a₂/C₁) is about 1.0, (b₂/C₁) is about 0.40, m₂ is about2.0, and n₂ is about 2.0.

In one embodiment, the end segment 434, segment CE, comprises a smallbut finite dimension and may be swept at the trailing edge angle Λ₂. Theend segment 434 may assist in stabilizing the tip vorticity and maintainthe vortex position close to the extreme tip, point E. As will berecognized by those skilled in the art, the length of segment CE isdetermined by the sizing and contour parameters described above.

FIG. 4B is a cross-sectional view of an airfoil section of the wing tip400 illustrated in FIG. 4A, taken along line M-M. The airfoil sectionmay be cambered and twisted to maintain an elliptic loading to theextreme tip and avoid flow separation along the highly swept curvedleading edge 420. Airfoil twist may be defined by a rotation angle ofthe airfoil chord about the tip trailing edge, CED, relative to the wingreference plane, x′-y′. In other embodiments, airfoil shapes may bemodified variations of the winglet airfoil disclosed herein withoutdeviating from the present invention.

FIG. 5 is an enlarged trailing-edge view of an exemplary embodiment of acurved tip section 500 of a wing 510 comprising a spanwise camber,according to embodiments described herein. In some embodiments, the wing510 may include a slight incline, a dihedral angle, ϕ_(D), 550, fromhorizontal 552, as the wing approaches the curved tip section 500. Insome embodiments, the geometry of the curved tip section 500 may also,or alternatively, incorporate a spanwise camber of the wing liftingsurface to maintain flow attachment, reduce flow separation, andminimize premature roll-up along the outer edge of the curved tipsection 500.

The camber may be defined in terms of a lateral displacement, z, of acurved trailing edge 522, CD, from a straight line extension of a wingtrailing edge 516, and may be defined by:z/C₁ =−P([y−y _(D)]/h−1)^(p).where C₁ is the length between point A 424 and point D 426, discussedabove in connection with FIG. 4A. In one embodiment, the parameters Pand p are selected in combination with the airfoil camber and twist anddefine the lifting surface between the previously defined curved leadingand curved trailing edges. In an exemplary embodiment characterized byoptimal performance characteristics, wherein the sizing parameters aregiven as described above, P is in the range of about 0.10 to about 0.25,and p is in the range of about 2.0 to about 4.0. More particularly, P isabout 0.15, and p is about 2.5. In other embodiments, the spanwisecamber may alternatively curve in the opposite, or positive z,direction. The above combination of parameters may be defined inrelation to the wing planform (i.e. sweep and taper) and aerodynamicloading so as to maintain elliptic loading and attached flow to curvedtip section 500. It will be appreciated that the design parameters maybe specified within appropriate limits so as to provide optimalperformance characteristics.

FIG. 6A illustrates a perspective view a representative wing 610 with awing end section 600 according to embodiments described herein asapplied to a winglet 660. The end of the wing may be turned upward in awinglet form 660, as illustrated more fully in FIG. 6B. In someembodiments, the winglet 660 may be attached to the end of the wing 610and may be comprised of any conventional design. For example, in theillustrated embodiment, the winglet 660 comprises a transition section662 out of the plane of the wing 610 into a vertical direction. Thetransition section 662 may be a continuous transition, as shown, such asalong a constant radius, parabolic, or an elliptical curve. In someembodiments, the transition section 662 may comprise a non-continuoussection. In the embodiment illustrated in FIGS. 6A-6B, the end of thewinglet 660, after the transition section 662, is substantially planar.Further, the wing 610 may be at an angle ϕ_(D) 650 from the horizontal652. A leading edge 612 and a trailing edge 616 are substantiallystraight within the plane of the wing 610 and through the transitionsection 662 until transitioning into the wing tip section 600. In theillustrated embodiment, the leading edge 612 and trailing edge 616merely transition into a vertical direction, thereby forming the winglet660.

As in the embodiment illustrated in FIG. 6A, the winglet 660 may includea curved leading edge 620, a curved trailing edge 622, and an endsegment 634. The curved leading edge 620 generally deviates from theupward turned tangential of the leading edge 612, while the curvedtrailing edge 622 deviates from the upward turned tangential of thetrailing edge 616. The curved leading edge 620 and the curved trailingedge 622 may be parabolic or elliptic. As will be appreciated, the endsegment 634 may be advantageously configured according to theembodiments described herein. Further, the winglet 660 may incorporateaspects of the spanwise camber, as illustrated in FIG. 6B. In theillustrated embodiment, the curved wing tip section 600 comprises only aportion of the winglet 660, and preferably is located at the end of thewinglet following the transition section 662.

FIG. 7 illustrates a perspective view of an airplane 700 comprising anexemplary embodiment of a propeller 702, in accordance with the presentinvention. As illustrated in FIG. 7A, the propeller tip geometrycomprises a curved leading edge 704, a curved trailing edge 706, and anend segment 708. The curved edges 704, 706 transition smoothly from apropeller blade body 710. In some embodiments, the curved leading edge704 may be designed according to embodiments described herein. Thecurved leading edge 704 may be parabolic or elliptic, and may beconfigured to maintain attached air flow and reduce flow separation.Further, the curved trailing edge 706 may also be configured accordingto embodiments described herein, and may follow a parabolic or ellipticcontour so as to maintain an appropriate chord variation and control thetrailing edge slope at the tip of the propeller 702. As illustrated inFIGS. 7-7A, the end segment 708 connects the end of the curved leadingedge 704 and the end of the curved trailing edge 706. The end segment708 generally comprises a finite dimension and is angled so as tostabilize tip vorticity and to maintain the trailing vortex position atthe tip of the propeller 702. It will be appreciated that the designparameters for the propeller 702 are substantially the same as for thevarious embodiments discussed above. Moreover, in other embodiments, thevarious embodiments described herein may be applied to duel propelleraircraft, wherein the propellers may be attached to the aircraft wings.

FIG. 8 illustrates a perspective view of a helicopter 800 comprising anexemplary embodiment of a rotor 802 according to the present invention.As illustrated in FIG. 8A, the rotor tip geometry comprises a curvedleading edge 804, a curved trailing edge 806, and an end segment 808.The curved edges 804, 806 transition smoothly from a rotor blade body810. In some embodiments, the curved leading edge 804 may be parabolicor elliptic, and id configured according to aspects of the abovedescribed embodiments so as to maintain attached air flow and reduceflow separation. Further, the curved trailing edge 806 may also beparabolic or elliptic, but may be designed with different parametersaccording to aspects of the present invention so as to maintain anappropriate chord variation and to control trailing edge slope at thetip of the rotor 802. The end segment 808 generally connects the end ofthe curved leading edge 804 and the end of the curved trailing edge 806,as illustrated in FIG. 8A. Generally, the end segment 808 comprises afinite dimension and is angled so as to stabilize tip vorticity and tomaintain the trailing vortex position at the tip of the rotor 802. Itwill be appreciated that the design parameters for the rotor 802 aresubstantially the same as for the various embodiments discussed above.

In some embodiments, a blended, or split, winglet may be used to producesuperior drag reduction and improvements in other aspects of airplaneperformance, as will be recognized by those skilled in the art. Further,embodiments of the split winglet, described herein, provide additionalperformance benefits with essentially no change in the structuralsupport needed beyond that required by the basic blended winglet design.Generally, the embodiments of the split winglet described below involveincorporating an additional surface, or ventral fin, below the wingchord plane. In one embodiment, the ventral fin is integrally configuredwith the curved winglet. In another embodiment, the ventral fin is anadd-on to an existing winglet.

FIGS. 9A-9C illustrate an exemplary embodiment of a split winglet 900.FIG. 9A is a front view of the split winglet 900 comprising a ventralfin 902 and an upper winglet 906. FIG. 9B illustrates a bottom view ofthe split winglet 900 and a lower surface of the ventral fin 902 of FIG.9A. FIG. 9C illustrates a side view of the split winglet 900 and anupper surface of the ventral fin 902. In the embodiment illustrated inFIGS. 9A-9C, the split winglet 900 comprises a primary surface attachedto the wing 904 at A and further comprises a near-planar outer panel B,a tip configuration C, and a transition section A-B between the wing 904and the outer panel of the winglet 900. The ventral fin 902 projectsbelow a chord plane of the wing 904 and comprises a ventral surface D.

In an exemplary embodiment, parameters affecting the geometry of thesplit winglet 900 may be varied within typical ranges (i.e., size (h₁),cant (ϕ₁), sweep (Λ₁), camber (E), and twist (θ)) without significantlycompromising optimization of the ventral surface D or overallperformance of the split winglet 900. The tip configuration, C, and thegeometry of each surface may be individually designed so as to providean elliptical tip loading corresponding to a loading of each surface ofthe split winglet 900.

The outer panel B is designed to carry most of the load during operationof the split winglet 900. In embodiment illustrated in FIG. 9A, theouter panel B is substantially planar, and projects upward from the tipof the wing 904 at a cant angle ϕ₁. A leading edge 910 of the outerpanel B is swept rearward at an angle Λ₁. The outer panel B extends to aheight h₁ above the plane of the wing 904. The transition section A-Bbetween the wing 904 and the outer panel B is configured to minimizeaerodynamic interference. In an exemplary embodiment, the transitionsection A-B comprises a near-radial curve having a curvature radius ofr. In a further exemplary embodiment, the tip configuration C isoptimized to provide an elliptical loading tip loading, as mentionedabove.

The ventral surface D is sized and oriented to conform to certainphysical constraints and optimized to provide a loading corresponding tomaximum benefit with minimal effect on the wing bending moment. Asillustrated in FIGS. 9A and 9C, the ventral fin 902 projects from thetransition section A-B of the split winglet 900 with a cant angle ϕ₂ andextends below the plane of the wing 904 by a distance h₂.

During operation of the split winglet 900, drag is advantageouslyreduced as compared with a blended winglet comprising the same sizeprimary surface as the primary surface B. In some embodiments, whereinthe ventral surface D comprises a height which is about 0.4 the heightof the primary surface B (i.e., h₂=0.4×h₁), drag may be reduced bysubstantially 2% or more. Other aerodynamic characteristics aresimilarly enhanced, thereby resulting in higher cruise altitudes,shorter time-to-climb, improved buffet margins, reduced noise, andhigher second segment weight limits without any adverse effects onairplane controllability or handling qualities.

As will be recognized by those skilled in the art, any improvement instructural stiffness characteristics of the wing 904 generally producesadditional drag benefits corresponding to a reduction in wingaeroelastic twist. Thus, the drag benefit may be increased if the wing904 has available structural margin or the wing 904 can be structurallymodified to allow increased bending moment. As will be appreciated, atradeoff between wing modification and drag reduction can be favorablefor modest increases in bending moment beyond that produced by thewinglet alone.

In some embodiments, the ventral fin 902 may be configured to emanatefrom the plane of the wing 904 at generally the same spanwise winglocation as the upper winglet 906. In other embodiments, the ventral fin902 may be configured to emanate from other locations along the winglet900, including along the transition section A-B or the lower facingsurface of the outer panel B. In an exemplary embodiment, the ventralfin 902 may be configured to emanate from a general midpoint of thetransition section A-B.

In some embodiments, the upper winglet 906 may continuously transitionfrom the wing 904. In an exemplary embodiment, illustrated in FIG. 9C,the upper winglet 906 comprises a transition section 914 which smoothlyextends from the upper and lower surfaces of the wing 904 along leadingand trailing edges of the wing 904, such that the upper winglet 906smoothly integrates with the surfaces and edges of the wing 904. Thetransition section 914 of the upper winglet 906 continuously andsmoothly curves toward the vertical so as to seamlessly transition froma profile of the wing 904 to a generally planar profile of the upperwinglet 906, as illustrated in FIG. 9A. The upper winglet 906 extends ina plane from the transition section 914 at an angle with respect tovertical and terminates at a winglet tip configuration 916. As bestillustrated in FIG. 9C, the leading edge 910 comprises a generallylinear section 912 swept at an angle Λ₁. As illustrated in FIG. 9C, theleading edge 910 continuously and smoothly transitions from the leadingedge of the wing 904, along the transition section 914, to the generallylinear section 912. At an upper end of the linear section 912, theleading edge 910 continues along a curved path into the winglet tipconfiguration 916, such that the leading edge 910 curves toward anairstream direction 918, which generally is parallel to the body of theairplane 102, as illustrated in FIG. 1. As illustrated in FIGS. 9B-9C,the trailing edge 920 is generally linear and transitions along a curvedand upward path, such that the trailing edge 920 continuouslytransitions from the trailing edge of the wing 904 to the winglet tipconfiguration 916. In other embodiments, however, the upper winglet 906may be swept and tapered to a greater extent than the wing 904.

As illustrated in FIGS. 9A-9C, the ventral fin 902 generally comprises aplanar projection below the upper winglet 906 which extends below theplane of the wing 904 at an angle ϕ₂ with respect to vertical. As bestillustrated in FIG. 9C, the ventral fin 902 is generally wing-shaped,such that the ventral fin 902 is swept and tapered. The ventral fin 902further comprises a leading edge 922 which extends generally linearlyfrom the upper winglet 906, then extends along a continuous curve towardthe airstream direction 918, and then terminates at a ventral fin tip928. In other embodiments, the leading edge 922 may be curved so as toreduce any discontinuity between the surfaces of the wing 904 and theventral fin 902. Thus, in some embodiments the leading edge 922 may bepositioned closer to the leading edge 910 of the upper winglet 906, thenextend away from the upper winglet 906, and then terminate at theventral fin tip 928.

In the illustrated embodiment of FIGS. 9B-9C, a trailing edge 924 of theventral fin 902 is generally linear, extending directly from the upperwinglet 906 and terminating at the ventral fin tip 928. In someembodiments, however, the trailing edge 924 may be curved, as discussedabove in connection with the leading edge 922. It will be recognizedthat configuring the trailing edge 924 as a curve serves to reduce anydiscontinuity between the trailing edge 920 of the upper winglet 906 andthe trailing edge 924 of the ventral fin 902. Further, the chord lengthof the ventral fin 902 at an attachment location with the upper winglet906 may be equal to or less than the chord length of the upper winglet906 at the attachment location. As illustrated in FIGS. 9B-9C, the chordlength of the ventral fin 902 is less than the chord length of the upperwinglet 906 at the attachment location. The trailing edge 924 of theventral fin 902 emanates from a point along the trailing edge 920 of theupper winglet 906, whereas the leading edge 922 of the ventral fin 902emanates from a bottom surface of the upper winglet 906.

In an exemplary embodiment, the split winglet 900 is integrated suchthat the upper winglet 906 and ventral fin 902 comprise a continuouswing tip structure. The upper winglet 906 therefore comprises an upwardprojecting surface and the ventral fin 902 comprises a lower projectingsurface. In some embodiments, the ventral fin 902 may project from alower surface of the upper winglet 906 at a near linear profile, asillustrated in FIG. 9A. The intersection of the upper winglet 906 andthe ventral fin 902 may be continuous so as to constitute a blendedintersection, thereby minimizing aerodynamic interference and producingoptimal loading. In other embodiments, the upper winglet 906 and theventral fin 902 may emanate from the same spanwise location of the wing904.

In some embodiments, the ventral fin 902 may comprise a componentseparate from the upper winglet 906 and be attached to either the wing904 or the upper winglet 906. The ventral fin 902 may be bolted orotherwise fastened to the tip of the wing 904. Further, the ventral fin902 may comprise a ventral surface D which is generally linear. In someembodiments, the ventral fin 902 may be attached to the upper winglet906 near a mid-point of the transition section A-B, such that theventral fin 902 extends below the wing 904.

FIG. 10 illustrates an exemplary load distribution 1000 for a wing 1004which includes a split winglet 1006, in accordance with the geometriesand design considerations described above in connection with FIGS.9A-9C. The split winglet 1006 comprises an upper winglet 1008 and alower ventral fin 1010. It will be recognized that the split winglet1006 is substantially similar to the split winglet 900, and thus theupper winglet 1008 comprises a primary surface B, and the lower ventralfin 1010 comprises a ventral surface D. As illustrated in FIG. 10, theload distribution 1000 is optimized with a loading of the primarysurface B being directed inboard and a loading of the ventral surface Dbeing directed outboard. It should be recognized that the loaddistribution 1000 provides a substantially maximum drag benefit for anycombination of primary and ventral surface sizing for which the loads donot exceed the structural capability of the wing 1004. The load of theprimary surface B and the load of the ventral surface D are generallyelliptical. As indicated in FIG. 10, the loading at the end of theprimary surface B and ventral surface D is greatest at the origin ofeach surface, indicated respectively as l _(1B) and l _(1D), andapproaches zero at the tip of each surface. The load of each surface atthe tip of the wing 1004, indicated as l ₁, is generally equal to thesum of the loading at the origin of the primary surface B and theventral surface D, (i.e., l _(1B)+l _(1D)).

FIGS. 11A-11B illustrate an exemplary embodiment of an integrated splitwinglet 1100, according to the present invention. FIG. 11A illustratesan exemplary front view of the winglet 1100, while FIG. 11B illustratesan exemplary side view. The exemplary integrated split winglet 1100 isconceived as a unit that may be attached directly to the wing tip atlocation A. However, it will be apparent to those skilled in the artthat the integrated split winglet is easily separable into two or moreparts, including a first, upper element 1102 which closely resembles ablended winglet and a second, lower element 1103, the ventral fin, whichis attachable to the upper element 1102 at a transition between the wingtip and the winglet upper element 1102 (i.e. transition section BC).

The upper element 1102 generally comprises an adapter section (AB), atransition section (BC), and a blade section (CD). The adapter sectionAB is configured to fit the split winglet onto an existing wing end, andgenerally corresponds to the wing surface extending from A. As viewedfrom above, the adapter section AB generally is trapezoidal. Thetransition section BC provides a continuous transition surface betweenthe extended wing surface at B and the blade section at C. In theillustrated embodiment of FIG. 11A, the transition section BC has aradius of curvature R. In some embodiments, the curvature of thetransition section BC may be variable. The blade section CD is generallyplanar and is designed to carry most of the load. The different sectionsof the upper element 1102 are serially connected, such that the upperelement 1102 comprises continuous leading edge and trailing edge curveswhich bound upper and lower surfaces of the upper element 1102 so as toform a solid body having an airfoil cross section.

As mentioned above, in some embodiments the transition section BC mayhave a variable radius along its length. Thus, the transition section BCmay be described in terms of an average radius, R_(A), and a minimumradius, R_(M), at any point along the transition. The transition sectionBC of the upper element 1102 may comprise an average radius ofcurvature, R_(A), of the principle spanwise generator and a minimumradius of curvature at any point, R_(M), which meets the criteria:

${R_{A/h} = {K_{A}\left( \frac{1}{\sqrt{1 + {\sin\mspace{14mu}\phi_{1\;}}}} \right)}},$where, K_(A) is preferably between 0.25 and 0.7 and more preferablybetween 0.25 and 0.35. A ratio of the minimum to the average radius,R_(M)/R_(A), is preferably between 0.3 and 1.0 and more preferablybetween 0.5 and 1.0.

The airfoil geometry of the transition section BC near the leading edgeis constrained by the following relationships between leading edge sweepangle, A, airfoil nose camber, η, and chordwise extent of nose camber,ξ_(T):

${{\eta/\eta_{0}} = \left( {1 - \frac{\xi}{\xi_{T}}} \right)^{2}};{0 < \xi < \xi_{T}}$η₀ = .1ξ_(T) = .006  tan^(1/3)Λ

The lower element 1103 generally comprises a ventral fin, EF. The lowerelement 1103 has a generally wing-like configuration attached to theupper element 1102. The lower element 1103 may be attached to the upperelement 1102 along the transition section BC at a generally 90° anglewhich facilitates adjusting the lower element 1103 relative to the localwing vector.

The general geometry of both the upper element 1102 (identified bysubscript 1) and the lower element 1103 (identified by subscript 2) aredefined by a height from the wing plane (h₁ and h₂); cant angle (ϕ₁,ϕ₂); incidence angle (i₁, i₂); sweep angle (Λ₁, Λ₂); and blade taper(λ₁, λ₂). It will be appreciated that the geometry determines theaerodynamic loading, which is critical to enhancement of the airplaneperformance characteristics. Generally, the geometric parameters areselected so as to minimize drag without incurring structural or weightchanges which might offset or compromise the drag benefits or adverselyaffect other characteristics. An optimization process results in theoptimum combination of independent geometric parameters while satisfyingthe constraints that apply to the dependent design parameters selectedfor a given application. The above identified parameters are mostlyindependent parameters, although they may be considered dependent forcertain applications. Additional dependent parameters may include, aloading split ratio, an allowable wing bending moment, an extent ofstructural modification, a winglet size, airplane operating limitations,economic and business requirements, and an adaptability. Generally, thedesign restrictions for optimization of the split blended winglet 1100will be more complex than the traditional blended winglet technology.

The upper and lower elements 1102, 1103 are each oriented at a cantangle with respect to the wing normal. The cant angle of the upperelement 1102 is generally between zero and fifty degrees (i.e.,0°<ϕ₁<50°), while the cant angle of the lower element 1103 is betweenninety and one hundred eight degrees (i.e., 90°<ϕ₂<180°).

Each of the first and second elements 1102, 1103 includes a taperednear-planar section. These sections include a taper ratio generally inthe range of approximately 0.28 and 0.33 for the first element (i.e.,0.28<λ₁<0.33) and approximately 0.33 and 0.4 for the second element(i.e., 0.33<λ₂<0.4). The split winglet includes a surface areacorresponding to a design lift coefficient C_(L) in the range ofapproximately 0.6 and 0.7 (i.e., 0.6<C_(L)<0.7) and a thickness ratiocorresponding to the section life coefficient which meets the followingcriteria at the design operating condition:Winglet M _(crit)=Wing M _(crit)+0.01

The leading edge and curves of both the upper and lower elements 1102,1103 each varies monotonically with a leading edge sweep angle (Λ₁, Λ₂)up to 65°. The leading edge curves and sweep angles are correlated withairfoil section nose camber so as to substantially prevent or reduceformation of leading edge vortices. The elements 1102, 1103 may belimited in cant angle, curvature, height or surface area so as tooptimize performance over the flight envelope with minimal impact onwing structural requirements which affect weight, cost, or airplaneeconomics.

FIG. 12 illustrates another embodiment of the split winglet design. Asillustrated in FIG. 12, a split winglet 1200 comprises a continuousprojection of a wing 1202 into an upper section 1204, extending abovethe plane of the wing 1202, and a lower section 1206 extending below theplane of the wing 1202. Leading edges of the upper and lower sections1204, 1206 emanate from a common point along the leading edge of the tipof the wing 1202. Trailing edges of the upper and lower sections 1204,1206 similarly emanate from a common point along the trailing edge ofthe wing tip. The leading edges of both the upper and lower sections1204, 1206 may comprise a generally linear portion with a smooth curvedtransition from the wing 1202 to the linear portion. The winglet tips ofthe upper and lower sections 1204, 1206 may curve toward a freeairstream direction 1208. The trailing edges may generally projectlinearly to the respective ends of the winglet sections 1204, 1206. Insome embodiments, the trailing edge of either or both of the upper andlower sections 1204, 1206 may further comprise a curved portionextending from the common point. It will be appreciated that the curvedportions reduce the chord length of the respective sections 1204, 1206,such that the upper and lower sections 1204, 1206 comprise a variabletaper and thus may be greater along a portion of the sections 1204, 1206than from the wing. In an embodiment, the upper surface of the wing 1202transitions continuously into an upper surface of the section 1204, andthe lower surface of the wing 1202 transitions continuously into a lowersurface of the section 1206. In another embodiment, the split winglet1200 further comprises a continuous junction between a lower surface ofthe section 1204 and an upper surface of the section 1206.

FIG. 13 illustrates and exemplary embodiment of a split winglet 1300comprising an upper section 1304 and a lower section 1306. The splitwinglet 1300 is substantially similar to the split winglet 1200,illustrated in FIG. 12, with the exception that the split winglet 1300comprises a different tip configuration 1302. In some embodiments, theupper and lower sections 1304, 1306 may comprise various features,including by way of non-limiting example, leading and trailing edges,winglet surface contours, a transition profile between the winglet andthe wing, and winglet tip profiles. As previously disclosed, the leadingand trailing edges of the winglet sections 1304, 1306 may comprisecontinuous extensions of leading and trailing edges of the wing.Further, the taper of the sections 1304, 1306 may also be greater thanthat of the wing and may be variable long its length. In someembodiments, utilizing continuous leading and trailing edge designs, atransition to the greater taper may occur along either the leading edge,the trailing edge, or a combination of both. In other embodiments, thelower section 1306 (i.e., the ventral fin) may comprise the samechordwise span as the upper section 1304 and wing, or may be reduced,such that either the leading edge and/or the trailing edge of thesection 1306 extends from a lower surface of either the wing or theupper section 1304. In some embodiments, the tip configuration 1302 maycomprise various formations or curvatures, depending on the application.In the embodiment illustrated in FIG. 13, an additional tip edge 1308 isincluded between the leading and trailing edges of the sections 1304,1306. In some embodiments, either or both of the leading and trailingedges may be curved toward the free airstream direction 1310.

FIG. 14 illustrates an exemplary use environment 1400 wherein anairplane 1404 comprises a split winglet 1408 installed onto a wing 1412of the airplane in accordance with an embodiment of the presentinvention. The split winglet 1408 comprises an upper winglet 1416extending from a tip of the wing 1412, above a chord plane of the wing,and a ventral fin 1420 projecting below the chord plane from a lowersurface of the upper winglet 1416. The split winglet 1408 illustrated inFIG. 14 is substantially similar to the split winglet 900 of FIGS.9A-9C, with the exception that the split winglet 1408 comprises an upperwinglet tip configuration 1424 and a ventral fin tip configuration 1428,both of which resembling a curved blade which is discussed in moredetail with reference to FIGS. 15-16. It should be understood, however,that the tip configurations 1424, 1428 may comprise various combinationsof segments, curvatures, or other geometric formations, depending on theapplication envisioned, without straying beyond the spirit and scope ofthe present invention.

FIGS. 15A-15C illustrate an exemplary embodiment of a split winglet 1500configured for installation onto a wing tip 1504 of an airplane inaccordance with the present invention. The split winglet 1500 comprisesan upper winglet 1512 extending from the wing tip 1504 above a chordplane of the wing and a ventral fin 1516 projecting below the chordplane from a lower surface 1520 of the upper winglet 1512. The splitwinglet 1500 illustrated in FIGS. 15A-15C is substantially similar tothe split winglet 900 of FIGS. 9A-9C, with the exception that the splitwinglet 1500 comprises an upper winglet tip configuration 1524 and aventral fin tip configuration 1528, as discussed below.

Similar to the upper winglet 906, the upper winglet 1512 generallycomprises a transition section 1532 which curves upward from the wingtip 1504 into a substantially planar section 1536. In an embodiment, thetransition section 1532 comprises a substantially constant radius ofcurvature between the wing tip 1504 and the planar section 1536. Inanother embodiment, the transition section 1532 comprises two or moreradii of curvature disposed along a length of the transition section1532 between the wing tip 1504 and the planar section 1536. In otherembodiments, the transition section 1532 may comprise a continuouslychanging radius of curvature along a length of the transition section1532 between the wing tip 1504 and the planar section 1536. In stillother embodiments, the transition section 1532 may comprise asubstantially nonlinear curvature along a length of the transitionsection 1532 between the wing tip 1504 and the planar section 1536.

The upper winglet 1512 further comprises an upper surface 1540 and alower surface 1544 proximally bounded by a leading edge 1548 anddistally bounded by a trailing edge 1552. The upper surface 1540 and thelower surface 1544 of the upper winglet 1512 are respective smoothextensions of upper and lower surfaces of the wing tip 1504, such thatthe leading and trailing edges 1548, 1552 of the upper winglet 1512 arerespectively continuous extensions of a leading edge and a trailing edgeof the wing 1504. As illustrated in FIG. 15C, the leading edge 1548 andthe trailing edge 1552 comprise substantially linear sections which areswept toward an airstream direction 1556 which is substantially parallelwith the root chord of the wing 1504. The leading and trailing edges1548, 1552 converge at the upper winglet tip configuration 1524.

In the illustrated embodiment, the upper winglet tip configuration 1524comprises a first curve 1560 of the leading edge 1548 having a firstradius and a second curve 1564 of the trailing edge 1552 having a secondradius. As best illustrated in FIG. 15C, the first and second curves1560, 1564 orient the leading and trailing edges 1548, 1552 toward theairstream direction 1556 so as to converge to substantially a point 1568distal of the wing tip 1504 of the airplane. It will be recognized thatthe first and second curves 1560, 1564 give the upper winglet tipconfiguration 1524 a curved blade shape. In another embodiment, thefirst and second curves 1560, 1564 may be considerably smaller than asillustrated in FIG. 15C, and coupled with suitable linear segments,thereby configuring the upper winglet tip configuration 1524 into any ofa variety of distally oriented protrusions. In some embodiments, thefirst and second curves 1560, 1564 may each be a compound curvecomprising two or more different radii, such that the leading andtrailing edges 1548, 1552 converge at the point 1568. In otherembodiments, the first and second curves 1560, 1564 may each comprise acontinuously changing radius of curvature along each of the curves 1560,1564, such that the leading and trailing edges 1548, 1552 converge atthe point 1568. In still other embodiments, the upper winglet tipconfiguration 1524 may comprise configurations other than shown anddescribed herein without detracting from the present invention.

Referring again to FIG. 15A, the ventral fin 1516 projects below thechord plane from the lower surface 1544 of the transition section 1532.Similar to the ventral fin 902, the ventral fin 1516 comprises an uppersurface 1572 and a lower surface 1576 proximally bounded by a leadingedge 1580 and distally bounded by a trailing edge 1584. The leading andtrailing edges 1580, 1584 comprise substantially linear sections whichare swept toward the airstream direction 1556 and then converge at theventral fin tip configuration 1528.

The ventral fin tip configuration 1528 is substantially similar to theupper winglet tip configuration 1524, with the exception that theventral fin tip configuration 1528 is generally smaller in size due tothe smaller dimensions of the ventral fin 1516 compared to the upperwinglet 1512. Similar to the upper winglet tip configuration 1524, inthe illustrated embodiment of the ventral fin tip configuration 1528,the leading edge 1580 and the trailing edge 1584 curve toward theairstream direction 1556 and then terminate at substantially a point1558 distal of the wing tip 1504 of the airplane. It should beunderstood that in other embodiments, the ventral fin tip configuration1528 may comprise a wide variety of configurations other than shown anddescribed herein without detracting from the present invention.

In the embodiment illustrated in FIGS. 15C-15C, the leading edge 1580 ofthe ventral fin 1516 merges into the lower surface 1544 of the upperwinglet 1512 distal of the leading edge 1548 of the upper winglet 1512,and the trailing edge 1584 merges into the trailing edge 1552 of theupper winglet 1512. In some embodiments, the leading edge 1548 of theupper winglet 1512 and the leading edge 1580 of the ventral fin 1516merge together at the transition section 1532, such that the leadingedges 1548, 1580 are continuous extensions of the leading edge of thewing 1504. In some embodiments, the trailing edge 1552 of the upperwinglet 1512 and the trailing edge 1584 of the ventral fin 1516 mergetogether at the transition section 1532, such that the trailing edges1552, 1584 are continuous extensions of the trailing edge of the wing1504. It will be recognized that the ventral fin 1516 may be coupled tothe upper winglet 1512 in a variety of diverse configurations, andthereby placing the edges of the upper winglet 1512, the ventral fin1516, and the wing 1504 into various relationships, without deviatingfrom the spirit and the scope of the present invention.

FIGS. 16A-16B illustrate an exemplary embodiment of a wingletretrofitting, whereby the upper winglet 906 illustrated in FIGS. 9A-9Cis modified so as to resemble the upper winglet 1512 illustrated inFIGS. 15A-15C. FIG. 16A is an enlarged section view of the upper winglet906 illustrating the winglet tip configuration 916, as shown in FIG. 9C.The winglet tip configuration 916 comprises a winglet tip cap 1604fixedly attached to the upper winglet 906 by way of a multiplicity offasteners 1608. FIG. 16B is an enlarged section view of the upperwinglet 906 after having been retrofitted with a curved blade cap 1616,thereby producing a curved blade tip configuration 1612 which resemblesthe upper winglet tip configuration 1524 illustrated in FIG. 15C. Itwill be appreciated that the curved blade cap 1616 is suitablyconfigured for installation onto the upper winglet 906 in place of thewinglet tip cap 1604. Generally, the fasteners 1608 and the winglet tipcap 1604 are removed from the upper winglet 906, and the curved bladecap 1616 is then installed onto the upper winglet 906 and secured by wayof the original fasteners 1608, thereby implementing the split winglet900 with an upper winglet which is substantially similar to the upperwinglet 1512 illustrated in FIGS. 15A-15C.

The curved blade cap 1616 comprises a first curve 1620 and a secondcurve 1624, both of which terminating at a distal segment 1628. Asdiscussed with reference to FIGS. 15A-15C, the first and second curves1620, 1624 may each be a compound curve comprising two or more differentradii, such that the leading and trailing edges of the curved blade cap1616 converge at the distal segment 1628. In other embodiments, however,the first and second curves 1620, 1624 may each comprise a continuouslychanging radius of curvature, such that the leading and trailing edgesof the curved blade cap 1620, 1624 converge at the distal segment 1628.In other embodiments, the curved blade cap 1616 may comprise a distalpoint, as illustrated in FIG. 15C, in lieu of the distal segment 1628.In still other embodiments, the curved blade cap 1616 may compriseconfigurations other than shown and described herein without detractingfrom the present invention. Moreover, it should be understood that thewinglet retrofitting illustrated in FIGS. 16A-16B is not limited solelyto the upper winglet 906, but rather a substantially similar retrofit tothe ventral fin 902 may be preformed, such that the ventral fin 902resembles the ventral fin 1516 illustrated in FIGS. 15A-15C.

While the invention has been described in terms of particular variationsand illustrative figures, those of ordinary skill in the art willrecognize that the invention is not limited to the variations or figuresdescribed. In addition, where methods and steps described above indicatecertain events occurring in certain order, those of ordinary skill inthe art will recognize that the ordering of certain steps may bemodified and that such modifications are in accordance with thevariations of the invention. Additionally, certain of the steps may beperformed concurrently in a parallel process when possible, as well asperformed sequentially as described above. To the extent there arevariations of the invention, which are within the spirit of thedisclosure or equivalent to the inventions found in the claims, it isthe intent that this patent will cover those variations as well.Variations contemplated within the scope of the invention includeembodiments incorporating one or more features of the various featuresdescribed herein in any combination without limitation. In addition,embodiments and features described herein may be used in other types ofapplications not specifically discussed, such as by way of non-limitingexample: water craft, other aircraft, or applications generally intendedto move gas or liquid. For example, water craft including propellers,helicopters, and propeller airplanes are all understood to benefit fromone or more embodiments described herein. Alternatively, fans, includingventilation systems, are also understood to benefit from one or moreembodiments described herein. Therefore, the present invention is to beunderstood as not limited by the specific embodiments described herein,but only by scope of the appended claims.

What is claimed is:
 1. A method of retrofitting a winglet, the wingletincluding a winglet leading edge and a winglet trailing edge, the methodcomprising: obtaining a curved blade cap, comprising: a blade capleading edge having a first curve with a first radius; a blade captrailing edge having a second curve with a second radius; and a distalsegment oblique to the first curve and the second curve, the first curveterminating at a first end of the distal segment and the second curveterminating at a second end of the distal segment opposite the firstend; and fastening the curved blade cap to the winglet, comprising:aligning the blade cap leading edge with the winglet leading edge; andaligning the blade cap trailing edge with the winglet trailing edge. 2.The method of retrofitting according to claim 1, wherein the wingletextends from a wing tip above a chord plane of a wing, the wingletcomprising an upper surface and a lower surface bounded by the wingletleading edge and the winglet trailing edge swept toward an airstreamdirection substantially parallel with a root chord.
 3. The method ofretrofitting according to claim 1, wherein at least one of the firstcurve and the second curve is a compound curve comprising at least afirst curve portion having a first radius and a second curve portionhaving a second radius.
 4. The method of retrofitting according to claim1, wherein at least one of the first curve and the second curvecomprises a radius of curvature that continuously changes as a functionof a length of the respective curve.
 5. The method of retrofittingaccording to claim 4, wherein both the first curve and the second curvecomprise a radius of curvature that continuously changes as a functionof a length of the first curve and the second curve.
 6. The method ofretrofitting according to claim 1, further comprising removing a tip capfrom the winglet prior to fastening the curved blade cap to the winglet.7. The method of retrofitting according to claim 1, wherein the curvedblade cap includes a first plurality of openings and the wingletincludes a second plurality of openings, further comprising: aligningthe first plurality of openings with the second plurality of openings;and inserting a fastener through each of the aligned first plurality ofopenings and second plurality of openings.
 8. A method of retrofitting,comprising: obtaining a curved blade cap, comprising: a blade capleading edge having a first curve with a first radius; a blade captrailing edge having a second curve with a second radius; and fasteningthe curved blade cap to at least one of a winglet and a ventral fin, thewinglet extending from a wing tip above a chord plane of a wing, thewinglet comprising an upper surface and a lower surface bounded by aleading edge and a trailing edge swept toward an airstream direction,the ventral fin projecting below the chord plane from the winglet, theventral fin comprising an upper surface and a lower surface bounded by aleading edge and a trailing edge swept toward the airstream direction,the fastening comprising: aligning the blade cap leading edge with atleast one of the winglet leading edge and the ventral fin leading edge;and aligning the blade cap trailing edge with at least one of thewinglet trailing edge and the ventral fin trailing edge.
 9. The methodof retrofitting according to claim 8, wherein the curved blade capfurther comprises a distal segment oblique to the first curve and thesecond curve, the first curve terminating at a first end of the distalsegment and the second curve terminating at a second end of the distalsegment opposite the first end.
 10. The method of retrofitting accordingto claim 8, wherein the fastening comprises fastening a first curvedblade cap to the winglet, and fastening a second curved blade cap to theventral fin.
 11. The method of retrofitting according to claim 8,wherein the winglet further comprises a transition section which curvesupward from the wing tip into a substantially planar section, whereinthe upper surface and the lower surface of the winglet respectively arecontinuous extensions of an upper surface and a lower surface of thewing tip, and wherein the leading edge and the trailing edge of thewinglet respectively are continuous extensions of a leading edge and atrailing edge of the wing.
 12. The method of retrofitting according toclaim 11, wherein the transition section comprises a substantiallyconstant radius of curvature between the wing tip and the substantiallyplanar section.
 13. The method of retrofitting according to claim 11,wherein the transition section comprises at least a first portion havinga first radius and a second portion having a second radius disposedalong a length of the transition section between the wing tip and thesubstantially planar section.
 14. The method of retrofitting accordingto claim 11, wherein the transition section comprises a curvature thatcontinuously changes as a function of a length of the transition sectionbetween the wing tip and the substantially planar section.
 15. Themethod of retrofitting according to claim 11, wherein the ventral finprojects from a lower surface of the transition section and extendsbelow the chord plane.
 16. The method of retrofitting according to claim11, wherein the ventral fin merges into the lower surface of the upperwinglet distal of the leading edge of the upper winglet.
 17. The methodof retrofitting according to claim 16, wherein the trailing edge of theventral fin merges into the trailing edge of the upper winglet.
 18. Themethod of retrofitting according to claim 11, wherein the leading edgeof the upper winglet and the leading edge of the ventral fin mergetogether at the transition section, wherein the leading edge of theupper winglet and the leading edge of the ventral fin are continuousextensions of the leading edge of the wing.
 19. The method ofretrofitting according to claim 11, wherein the trailing edge of theupper winglet and the trailing edge of the ventral fin merge together atthe transition section, wherein the trailing edge of the upper wingletand the trailing edge of the ventral fin are continuous extensions ofthe trailing edge of the wing.
 20. The method of retrofitting accordingto claim 8, wherein the curved blade cap includes a first plurality ofopenings and the at least one of the winglet and the ventral finincludes a second plurality of openings, further comprising: aligningthe first plurality of openings with the second plurality of openings;and inserting a fastener through each of the aligned first plurality ofopenings and second plurality of openings.